The Celtics should have a “please, pardon our appearance” sign on the parquet. What they’re trying to build is a team equipped to compete in April, May, and June and dethrone the Miami Heat. That can’t happen if the team is relying only upon the New New Big Three of Kevin Garnett, Paul Pierce, and Rajon Rondo.

It requires an invested and involved Jeff Green, who doesn’t shy away from shots. It needs Jason Terry reprising his sixth-man extraordinaire role, not in the starting lineup. It demands a healthy Avery Bradley to provide a running mate for Rondo and on-the-ball defense.

Like any work in progress, it also requires some moments of inscrutable progress, exasperation, and doubt that the finished product will be what was envisioned and worth the trouble. There was a lot of trouble at TD Garden on Wednesday night, but in the end it was worth it, and a 117-115 double-overtime victory over the Dallas Mavericks.

The goal for Rivers, who attended the Patriots’ 42-14 demolition of the Houston Texans on Monday night, should be to take a page out of the playbook of his coaching buddy Bill Belichick and have his team peaking at the opportune time. That’s not December.

After 21 games last season, the Celtics were 11-10. They were two games under .500 at the All-Star break. They were still one win away from the NBA Finals.

This season, they’re 12-9. It doesn’t matter.

Wednesday night’s tug-of-war was a microcosm of the Celtics’ season, the potential is palpable, the flaws are visible.

“You know, I told the guys I’m proud of them,” said Rivers. “I thought we made some mistakes that later on in the year we can’t make down the stretch of games. A foul to give, didn’t call a timeout and passed the ball, so we couldn’t advance it before the first overtime. Those are plays that can’t happen, but through all those mistakes we still won the game. So, as a coach you’ll take that.”

This was a maddening, invigorating, entertaining basketball game. The Celtics forced the Mavericks into a season-high 28 turnovers, nine from O.J. Mayo. They won a game in which they shot 43 percent from the field to Dallas’s 51 and were outscored in the paint, 60-40.

The Celtics had a dreadful time trying to contain Mavericks blur Darren Collison, who looked like he had a Fast Lane pass in the second half and the overtimes, scoring 16 of his 20 points.

The teams were tied, 96-96, at the end of regulation and, 105-105, after the first overtime. Neither team wanted to lose. Neither team was capable of the execution required to win.

“It shows that we have what it takes — even when a team made a run — to still get the win,” said Green, who had 15 points and more importantly kept shooting after being 2 of 10 in the first three quarters. “We caught some breaks . . . but we got it done. That’s all that matters.”

The Mavericks, coached by former Celtic Rick Carlisle, are missing franchise foundation piece Dirk Nowitzki, who is still out following arthroscopic surgery on his right knee. That meant we were spared the hoops heresy of inimitable Celtics announcer Cedric Maxwell insisting that Nowitzki is a better player than Larry Bird. Max, you are always must-listen, but you’ve got to let that one go.

The Celtics nearly let this one go.

After leading by as many as 14 in the third quarter, Boston was tied at 92 with 2:20 to go in a game in which it had never trailed. The Celtics found themselves behind on the scoreboard for the first time when old Lakers nemesis Derek Fisher drilled a 3-pointer that put Dallas up, 95-94, with 1:47 to go. Fisher fouled out in the first overtime and wasn’t around for the finish.

The Celtics led, 105-103, with 19 seconds left in the first overtime, but Mayo (24 points) sent it to a second OT with a determined drive with 11.1 seconds left.

In the second OT, Pierce, who had 16 points in the first half but was lost in the second, had 8 of the team’s 12 points. The captain matched his uniform number with a team-high 34 points, 12 in the overtimes.

Rondo’s drive and lay-in with 35 seconds left gave the Celtics a 110-107 lead. The fearless point guard, who finished with another triple-double near miss, then rebounded a Collison miss. Pierce made 1 of 2 free throws to put the Celtics up by 4 with 19.3 seconds left.

But like gum stuck to the bottom of a sneaker, the Mavericks just wouldn’t be scraped off.

Vince Carter hit a hanging 3-pointer in front of the Celtics’ bench, which had Rivers apoplectic that the Celtics hadn’t fouled. Pierce made a pair of free throws to put the Celtics up by 3 (113-110) with 8.3 seconds left.

Rivers wasn’t taking any chances on the next Dallas possession as he ordered his charges to foul and make the Mavericks earn it from the free throw line.

Dallas made it 113-112 on a pair of Collison free throws, but Pierce made his at the other end. Then Collison threw away the inbounds pass.

The Celtics could exhale.

Messy wins like these are a necessary part of the process of building a championship contender.

Christopher L. Gasper is a Globe columnist and the host of Boston Sports Live. He can be reached at cgasper@globe.com. Follow him on Twitter @cgasper.

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